BuchholzThis is the sum of opponents' scores. The idea is that the same score is
more valuable if achieved against players with better performances in a given
tournament.
Looks like an ideal tie-breaking method and has been used since the Swiss system
was invented.
However it has some weaknesses which are addressed by other methods (see
Median-Buchholz, Progress, Berger below).

Median-BuchholzSame as above but after leaving out the highest and the lowest scoring
opponents. Swiss Perfect allows configurable number of highest and lowest
scoring opponents to be left out (0,1 or 2)
Its idea is to eliminate distortions in Buchholz values caused by taking into
account games against run-away winners and bottom placed players.

Progressive ScoreCalculated by adding points from a progress table eg if your scores were:
Win, Loss, Win Draw then your progressive scores are 1, 1, 2, 2.5 and your
Progress tie-break value is 6.5
This is an attempt to put a higher value on scores which were achieved by
scoring better in the initial rounds than by finishing from behind. It is common
knowledge that the latter is usually much easier to achieve.
The problem is that the order of the Progress tie-breaks is known before the
last round (last round scores will change the actual value but not the order
within a point group). This may encourage some undesirable tournament "tactics"
in the last round.

FOR ROUND ROBIN -

Berger; Number of Wins.

BergerThis is calculated by adding scores of the opponents who were beaten by a
given player and half the scores of the opponents who she drew with. This has
been adopted from round-robin tournaments and is usually used as a secondary
method.

Number of WinsCalculated by adding a point for a win and nothing for a loss or a draw.
Intended to discourage making quick draws. Popular in 70's and early 80's
(particularly in round-robins). These days hardly justified.